Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20265887 | C2 | semidirect |
| 2. #20265531 | C2 | semidirect |
| 3. #20265527 | C2 | semidirect |
| 4. #20265484 | C2 | semidirect |
| 5. #20265467 | C2 | semidirect |
| 7. #20265379 | C2 | semidirect |
| 8. Q8×#11717579 | C2 | semidirect |
| 9. C4×#13108061 | C2 | semidirect |
| 11. #556×C101 | C2 | semidirect |
| 121. C101 | #3360 | semidirect |
| 122. #556 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265887 | 2 |
| #20265531 | 2 |
| #20265527 | 2 |
| #20265484 | 2 |
| #20265467 | 2 |
| #20265389 | 2 |
| #20265379 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108061 | 2 |
| C4×#13108059 | 2 |
| #556×C101 | 2 |
| #3360 | 101 |